Here is a bit more analysis of the data set used by Reinhart and Rogoff (R-R) and by Herndon Ash and Pollin (HAP) in their critique, and in particular the stata data set RR-processed.dta with data on public debt to GDP ratios and real GDP growth in 20 developed countries since 1946. This post is a minor addition to my earlier post and, especially adds little not shown by Arindrajit Dube.

In general macroeconomists have a problem that we non experimental data so we observe correlation but we want to know about causation. We don’t know what to do about this problem, so we almost all do the simplest thing which is look at timing — the cause comes before the effect. This is what Dube did showing a much stronger relationship between the public debt to gdp ratio and real GDP growth in the preceding 3 years than between the ratio and growth in the following three years. Also the non parametric estimate suggest a much stronger relationship between higher debt and lower subsequent growth for low levels of debt (up to 30% of GDP) than for higher levels — the opposite of what policy makers guessed given the original Reinhart and Rogoff analysis which really didn’t address that issue.

I redo Dube with parametric regressions which have the nice feature that there are standard statistical tests of null hypotheses concerning parametric point estimates (that’s fancy talk for STATA gives me t-statistics). The very first standard way to look at causality using post hoc ergo propter hoc is caused a Grander causality test. It is just a regression of one variable on lagged values of the explanatory variable and lagged values of the dependent variable. This is definitely the first thing macroeconomists do does if he she or they wonder about the direction of causality.

Recall the basic regression which notes that a debt to GDP ratio 1% higher is associated with a real GDP growth rate which is 0.02% lower (this is in fact a big deal).

dRGDP is the rate of growth of real GDP in the country, debtgdp is the ratio of public debt to gdp.

Now l1drgdp is the rate of real GDP growth lagged one year.

Including that variable appears to show a striking decline in the coefficient on the debt to GDP ratio, but really one should calculate the long term effect of a permanent increase in the debt ratio using

(1-0.3793671)(new steady state growth rate) = constant -0.089041(debt to GDP ratio) so the estimated long term effect is about -0.015 not much smaller than the simple coefficient.

The t-statistic is calculated assuming that the disturbance to growth is independent across countries (no global recessions or oil shocks) and that all structure within a country is captured by the simple lagged term. STATA is very willing to recalculate standard errors assuming, for example, that disturbances in the same year may be correlated.

. reg dRGDP debtgdp l1drgdp, cluster(Year)

gives a t-statistic on the debt to GDP ratio of -2.45 (the point estimates are exactly the same the cluster option just calculates more robust estimates of the standard errors). No big change.

Now I can get the t-statistic to be insignificant (you can always do this). I do this by definining a new lagged variable al3drgdp which is the average of the growth rate of real GDP lagged one, two, and three years. When I toss that in the regression and calculate standard errors allowing correlation in the same year across countries I get the t-statistic insignificant.

There is nothing wrong with this regression, except that I fiddled till I got the absolute value of the t-statistic under one (the added variable is due to Dube so there is that). The point estimate of the effect on growth isn’t much lower. the long run guess is a bit below 0.01 so slightly less than half the estimate based on the simple regression.

There is nothing much to see here. Neither strong evidence that the original estimate is due to reverse causation nor strong evidence that high debt causes low growth.